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6 marksComplex Numbers

CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2 · Question 1(a)(ii)

A quadratic equation ax^2 + bx + c = 0 has real coefficients a, b, c, with complex roots alpha = 1 - 3i and beta.

Hence, show that an equation with roots 1/(alpha - 2) and 1/(beta - 2) is given by 10x^2 + 2x + 1 = 0.

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Other parts of this question

  1. 1(a)(i)Calculate (alpha + beta) and (alpha * beta).[3 marks]
  2. 1(b)(i)Complete the Argand diagram to illustrate u.[1 mark]
  3. 1(b)(ii)On the same Argand plane, sketch the circle with equation |z - u| = 3.[2 marks]
  4. 1(b)(iii)Calculate the modulus and principal argument of z = (u / v)^5.[6 marks]
  5. 1(c)Determine the x-coordinates of the two stationary values of f.[7 marks]

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